1. 1.2 Types of Variables Definition: Qualitative variables measure a quality or characteristic on each experimental unit. Examples: Eye color, state of residence, gender, degree objective (BS/BA, MA, MBA, Ph.D.) Definition: Quantitative variables measure a numerical quantity or amount on each experimental unit. Examples: Height, weight, systolic blood pressure, number of weeds/square meter in a wheat field, number of defective items in a carton of 20 n Qualitative variables produce data that can be categorized according to similarities or differences in kind; they are often called categorical data, e.g., eye color, state of residence. © 1998 Brooks/Cole Publishing/ITP

2. Definition: A discrete variable can assume only a finite number of values, e.g., number of weeds, number of defective Definition: A continuous variable can assume the infinitely many values corresponding to the points on a line interval, e.g., height, weight. © 1998 Brooks/Cole Publishing/ITP

3. 4. The winning time for a horse running in the Kentucky Derby 5. The number of children in the fifth-grade class who are reading at or above grade level. © 1998 Brooks/Cole Publishing/ITP Figure 1.1

4. Example 1.9 Examine the three dotplots generated by Minitab and shown in Figure 1.11. Describe these distributions in terms of their locations and shapes. © 1998 Brooks/Cole Publishing/ITP Figure 1.11 Character Dotplots

5. 1.5 Relative Frequency Histograms Definition: A relative frequency histogram for a quantitative data set is a bar graph in which the height of the bar represents the proportion or relative frequency of occurrence for a particular class or subinterval of the variable being measured. n The class or subintervals are plotted along the x axis. © 1998 Brooks/Cole Publishing/ITP

6. Example 1.11 Twenty-five households are polled in a marketing survey, and Table 1.12 lists the numbers of quarts of milk purchased during a particular week. Construct a relative frequency histogram to describe the data. Table 1.12 0 3 5 4 3 2 1 3 1 2 1 1 2 0 1 4 3 2 2 2 2 2 2 3 4 Solution The variable being measured is “ number of quarts of milk,” which is a discrete variable that takes on only integer values. In this case, it is simplest to choose the classes or intervals as the integer values over the range of observed values: 0, 1, 2, 3, 4, and 5. © 1998 Brooks/Cole Publishing/ITP

7. Table 1.13 shows the classes and their corresponding frequencies and relative frequencies. The relative frequency histogram, generated using Minitab, is shown in Figure 1.14. Table 1.13 NumberRelative of Quarts Frequency Frequency 02.08 15.20 29.36 35.20 43.12 51.04 © 1998 Brooks/Cole Publishing/ITP

8. Figure 1.14

9. Interpreting Graphs with a Critical Eye: n What to look for as you describe the data: - scales - location - shape - outliers n Distributions are often described by their shapes: - symmetric - skewed to the right (long tail goes right) - skewed to the left (long tail goes left) - unimodal, bimodal, multimodal (one peak, two peaks, many peaks) © 1998 Brooks/Cole Publishing/ITP